Question

If two more red dots are to be placed on the grid, in how many ways can they be placed such that the image is symmetric?


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Answer 1

Answer:

With this one observation, and a little knowledge of combinations, we are now able to answer Question 1. The path must consist of 10 moves, five of which should be down and five of which should be right. In fact, the order of the moves does not matter as long as there are a total of 10 moves, five of which are right. By using combinations we can find the total number of ways we can “select” a right move from the collection of 10 moves (five right, five down).

10 Choose 5 = 252

There are 252 unique paths.

Note: we could have also used the down moves in place of the right moves.

Answer 2

Answer:

In fact, the order of the moves does not matter as long as there are a total of 10 moves, five of which are right. By using combinations we can find the total number of ways we can “select” a right move from the collection of 10 moves (five right, five down). There are 252 unique paths.